K. Kirsten et al., EFFECTIVE LANGRANGIAN FOR SELF-INTERACTING SCALAR FIELD-THEORIES IN CURVED SPACETIME, Physical review. D. Particles and fields, 48(6), 1993, pp. 2813-2822
We consider a self-interacting scalar field theory in a slowly varying
gravitational background field. Using zeta-function regularization an
d heat-kernel techniques, we derive the one-loop effective Lagrangian
up to second order in the variation of the background field and up to
quadratic terms in the curvature tensors. Specializing to different sp
acetimes of physical interest, the influence of the curvature on the p
hase transition is considered.